A man had three daughters. Another man asked him the ages of his daughter. He told that the product of their ages is 36.
Second man was confused and asked for another clue. First man told him that the sum of their ages is equal to his house number.
Second man did some calculations and was still confused. He asked for another clue. First man told him that his youngest daughter had blue eyes. On hearing this, second man immediately gave the correct Ans
Question : What are the ages of his daughter ?
To begin with, there is a small logical assumption that all the ages are integers.
Further to this, it is given that the product of the daughters' ages is 36. This gives the man just 8 possibilities:
AGE 1 AGE 2 AGE 3 SUM OF AGES
1 1 36 38
1 2 18 21
1 3 12 16
1 4 9 14
1 6 6 13
2 2 9 13
2 3 6 11
3 3 4 10
The correct solution has to exist within this range possibilities because the man could guess the same.
Calculation of the sum of their ages (the rightmost column) shows the only possible instances of the house no. If the sum were 38, 21, 16, 14, 11, or 10, he would have been able to guess the ages immediately. He was not able to do so only because the number of the house and the sum of the ages was 13! (This is because, even after this hint the solution was not unquely deducible…!!) Because of this, he did not have a unique solution until the man informed her about his youngest daughter.
It becomes clear that there is no ambiguity at this "youngest"position and that not two of them are tied at this position ( in case the ages would have been 9,2, and 2) . This is possible only if Kiran's daughters are 1, 6, and 6 years old.
With similar arguments, assuming no tie at the eldest position the correct set of ages would be 9, 2, 2.